Question: Simplify the following expression: $q = \dfrac{-5k^2 + 40k - 35}{k - 1} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ q =\dfrac{-5(k^2 - 8k + 7)}{k - 1} $ Then we factor the remaining polynomial: $k^2 {-8}k + {7} $ ${-1} {-7} = {-8}$ ${-1} \times {-7} = {7}$ $ (k {-1}) (k {-7}) $ This gives us a factored expression: $\dfrac{-5(k {-1}) (k {-7})}{k - 1}$ We can divide the numerator and denominator by $(k + 1)$ on condition that $k \neq 1$ Therefore $q = -5(k - 7); k \neq 1$